What is sqrt(7-2\sqrt{6)} ?

The solution to sqrt(7-2\sqrt{6)} is sqrt(6)-1

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Popular >

simplify sqrt(7-2\sqrt{6)}

simplify

7 - 26

6 - 1

Decimal Notation

1.44948 \dots

Solution steps

7 - 26

= 6 - 26 + 1

= (6)^{2} - 26 + (1)^{2}

1 = 1

= (6)^{2} - 26 + 1^{2}

26 \cdot 1 = 26

= (6)^{2} - 26 \cdot 1 + 1^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(6)^{2} - 26 \cdot 1 + 1^{2} = (6 - 1)^{2}

= (6 - 1)^{2}

Apply radical rule:

(6 - 1)^{2} = 6 - 1

= 6 - 1

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